In regards to the 2-stroke or 4-stroke I would pick the 4-stroke first choice, but the newer 2-strokes aren't too bad to troll with. Mine is a 225 optimax (2007) on a 22' boat and it trolls at 3.2mph no wind and 2.8 usually against the wind. That's just a hair higher than you should troll with umbrella rigs but it works just fine without have a plate (or 5 gallon bucket) to slow it down. It does not load up at all, I can troll for 2 hrs straight then hammer throttle to take off and no burbling or coughing it just takes off. Never had fouled a plug or even loaded up it burns pretty clean. With that being said though my next boat will have a 300 4-stroke verado just because of it being quite.
Older 2-strokes however won't troll for long periods of times without loading up. If looking at a new boat and gonna use your big motor to troll and not have a kicker motor be careful with your hours because your warranty will be cut premature due to too many hours. Now I use my boat a lot, but trolling put some extra hours on my motor when I took it in the first year I started striper fishing I had 285 hrs in 1 year, that is way more than your average fishing boat.
But either way you go if its a newer motor 2005ish and above you should be fine.